Class Notes: Subtracting a Whole Number from a Fraction

Objective

Learn how to subtract a whole number from a fraction by converting the whole number into a fraction and using common denominators.

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Steps for Subtracting a Whole Number from a Fraction

1. Write the Whole Number as a Fraction

   • Example: (2 = \frac{2}{1})

2. Convert to Common Denominators

   • Multiply the whole number fraction so the denominators match.

3. Subtract the Numerators

   • Once denominators are the same, subtract the numerators and keep the denominator.

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Example 1

Problem:
(\frac{14}{3} - 2)

• Convert 2 to a fraction:
  (2 = \frac{2}{1})

• Match denominators:
  Multiply (\frac{2}{1}) by (\frac{3}{3}):
  (\frac{2}{1} \times \frac{3}{3} = \frac{6}{3})

• Subtract:
  (\frac{14}{3} - \frac{6}{3} = \frac{8}{3})

• Answer:
  (\frac{8}{3}) (improper fraction)

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Example 2

Problem:
(\frac{3}{4} - 5)

• Convert 5 to a fraction:
  (5 = \frac{5}{1})

• Match denominators:
  Multiply (\frac{5}{1}) by (\frac{4}{4}):
  (\frac{5}{1} \times \frac{4}{4} = \frac{20}{4})

• Subtract:
  (\frac{3}{4} - \frac{20}{4} = \frac{-17}{4})

• Answer:
  (\frac{-17}{4}) (improper fraction)

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Key Points

• Always write the whole number as a fraction over 1.
• Find a common denominator by multiplying as necessary.
• Subtract the numerators once the denominators match.
• The final answer will be an improper fraction.